Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
335 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#4130 | C2 | semidirect |
| 3. C5×#3999 | C2 | semidirect |
| 4. C2×C52×Q8 | C4 | semidirect |
| 7. C2×C5×D20 | C4 | semidirect |
| 9. C2×C4×C5×D5 | C4 | semidirect |
| 14. #65785 | C5 | direct (N × H) |
| 31. #4130 | C2×C5 | semidirect |
| 33. #3999 | C2×C5 | semidirect |
| 48. C2×C5×Q8 | C4×C5 | semidirect |
| 49. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 56. C2×D20 | C4×C5 | semidirect |
| 58. C2×C4×D5 | C4×C5 | semidirect |
| 103. C52 | #410 | semidirect |
| 129. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 161. C5 | C5×#410 | semidirect |
| 162. C5 | #65785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C5×#4130 | 2 |
| C5×#3999 | 2 |
| #65785 | 5 |
| C5×#410 | 5 |